Abstract
The presented discourse develops a new model named rigid body oscillator. This model plays the same role in Eulerian mechanics as the model of nonlinear oscillator in Newtonian mechanics. The importance of introducing a rigid body oscillator, or in other words a rigid body on an elastic foundation of general kind, was pointed out by many scientists. However, the problem is not formalized up to now. In the paper, all concepts necessary for a mathematical description are introduced. Some of them are new. The equations of motion are represented in an unusual form for rigid body dynamics, have simple structure, but contain a nonlinearity of complicated kind. These equations may be an interesting object for the theory of nonlinear differential equations. The solutions of some problems are presented. For the simplest case, the exact solution is found by an explicid integration of the basic equations.
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